USCIS Definitions for Expedited Naturalization
Regularly Stationed Abroad means your spouse's employment will continue abroad for at least one year after the date that you will be naturalized. This should be clearly indicated on the employment contract your spouse holds, and the contract must be for the overseas work. If it is possible, you should file your application prior to your departure overseas. However, if you are already overseas, you should make sure that you meet the eligibility requirement of having at least one year remaining overseas at the time of naturalization. This is considered from the time you file your application, so you should only file if the end date of your spouse's employment contract will allow this one year of remaining time abroad.
Employers (Non-Military) for expedited naturalization cases must adhere to strict guidelines. This means that a qualified employer can be an American institution of research recognized as such by the Attorney General. The employer may also be an American-owned firm or corporation engaged in the development of foreign trade and commerce for the United States, a public international organization of which the United States is a member by law or treaty, or a religious denomination or an interdenominational organization with a valid presence in the United States.
U.S. Government Agencies (Non-Military) or civilian government agencies are staffed by civilians and are non-military entities. A list of these agencies can be found here:
For expedited naturalization, you would need a letter on official agency/department letterhead that states the facts of your spouse's employment, the basis of your spouse's hire (contract, permanent employee, etc.), and the length of your spouse's overseas employment.